Strategy-proofness, efficiency, and the core in matching problems with transfers

Abstract

We study a class of matching problems in which monetary transfers are possible. In this paper, we establish a close connection between the core and the existence of desirable rules that satisfy strategy-proofness or one-sided strategy-proofness. In our main result, we show that the optimal core is a unified lower bound of welfare for the existence of rules that satisfy strategy-proofness (or one-sided strategy-proofness), efficiency, individual rationality, and no subsidy. Applying this result, we also obtain impossibility and characterization results in our environment.